odecor good y) and one firm. Consumer 1 has only 10 units of good x as her endowment. Consumer 2 has 25 units of good y as her endowment. The firm produces good x by using good y. Its production function is x = 2√. Consumer 1 fully owns the firm. Consumer 1's utility function is given by U₁[1, 1] In ₁+In y₁. Consumer 2's utility function is given by U2[2, 32] = √√√2Y2. Let p be the price of good x and q the price of good y. Derive the general equilibrium. =
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- Consider an economy with two consumers A and B, one firm and two goods, 1 and 2. The initial endowments of A and B are w = wB = (1/2, 1/2). The utility functions are: u^(rf, 12) = In z{' + In r and "(f.) = Vzf + V=? The firm produces good 2 using good 1 as input, the production function is y2 = The consumer B owns the firm (denote z the firm's profit). Good 2 is the numeraire good (i.e., p2 = 1). (a) Determine the demand for good 1 of the consumers and the firm. (b) Show that there is a unique equilibrium price p. (c) Prove or disprove that the final allocation is Pareto Optimal.Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 2 units of good X and 6 units of good Y. Consumer B is given an initial endowment of 6 units of good X and 2 units of good Y. Consumer A's utility function is given by: UAXY) = X"Y, and consumer B's utility function is given by: Ug(X,Y) - MIN (2X, Y). If the prices are Px-1 and Py- 2, if each consumer sells her initial endowment and buys back her and in the optimal bundle, then in the Market for Good X there is Select) Market for Good Y there is [Select)Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 5 units of good Y. Consumer B is given an initial endowment of 5 units of good X and 3 units of good Y. Consumer A's utility function is given by: UA(X,Y)= X + 4Y, and consumer B's utility function is given by UB(X,Y)= MIN (X, 2Y). If the prices are Px = 1 and Py = 3, if each consumer sells her initial endowment and buys back her optimal bundle, which of the following statements is true? Group of answer choices Both Markets are in Equilibrium There is Excess Demand in the Market for Good X = 2.4 There is Excess Demand in the Market for Good Y = 0.8 There is Excess Supply in the Market for Good Y = 1.6 There is Excess Supply in the Market for Good X = 1.6 E
- Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(x1, x2) = In ¤1 + In x2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf, y½) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (y7, vž) = (38, 12(1 – B)). The hunter-gatherers now have the possibility of opening up their economy to free trade. In world markets, 1 unit of meat can be exchanged for 2 units of berries, and the country would be a price-taker. Which of the following statements is correct? O a. Only agents of type g benefit from free trade. O…= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.Consider an general equilibrium endowment economy with two goods and two individuals. The two individuals A and B have the following endowments {(w^, w), (wP, w? )} = {(4,3), (2, 1)} The utility functions for A and B are: U^(*f, a) = 0.5 log(x†)+log(x;) U® x? ,a?) = log(x)+0.5 log(xž) ** Part a (10 State the market clearing conditions. ** Part b ( Draw the Edgeworth box, including: • the x-y coordinates of the 4 corners. • the x-y coordinates of endowment point. • a sketch of some indifference curves for both individuals. ** Part c (10 Given the relative price p > 0, find the demand of good 1 for both individuals.
- 4) Consider a pure exchange economy with two goods, (x, y), and two consumers, (1, 2). Consumers' endowments are e1 = (4, 2) and e? = (6, 6) And their preferences are represented by utility functions: u(x, y) = x³y and u(x,y) = x³y$ (d) Set up the utility maximization problem for each consumer and solve for their Marshallian demand functions. (e) Compute the market demand for each good. () State the Walrus law for this economy and explain its economic interpretation. (g) Assume the excess demand for good x is zero, i.e., EDx = 0, and calculate the ratio of prices, i.e., p Ipy . Then, use this ratio of prices to show that the excess demand for good Yis also zero, i.e., EDy= 0. Briefly explain how this relates to the Walrus' law. (h) Given the price ratio found above, calculate the equilibrium allocations and show that feasibility, individual rationality, and Pareto efficiency holds.Astrid’s utility function is UA(HA,CA) = HA · CA. Birger’s utility function is UB(HB,CB) = min{HB , CB }. If Astrid’s initial endowment is no cheese and 5 units of herring and if Birger’s initial endowments are 6 units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese is the numeraire, it must be that demand equals supply in the herring market. This implies that i. 6/(p+1)+2.5=5. ii. 5/6 = p. iii. 6/p + 5/2p = 5. iv. 6/5 = p. v. min{5, 6} = p. The answer is i. Please show me how to get the answer. thank you!5. Consider an Edgeworth box economy where preferences are given by u'(x},*}) = x}x and uai,) = xf, (a) Suppose the initial endowments are e' = (4,4) and e² = (1,1). Find all the Pareto optimal allocations. (b) Suppose the initial endowments are e' = (5,5) and e = (0,0). Find all the Pareto optimal allocations.
- Please answer the question fully and completely else I will rate negative, thanks! Question 3 Consider an economy with two consumers, A and B, two goods called 1 and 2 and one firm. Consumers A and B are each endowed with a unit of each good. The utility functions of each consumer are: A: 13 4 4 u (x₁‚x2 ) = lnx₁ + Inx2 B:u ₁₂ (x, ‚ x 2 ) = x, x 2 The firm B 1 A 1 1 2 produces good 2 using good 1 as an input, according to the production function f(y) = y where y is the quantity of good 1. Consumer A is the sole shareholder of the firm and the firm operates to maximize profit. Page 2 If P₁ and P2 determine the utility maximizing demand of consumer are the per unit prices of goods 1 and 2, . B for each good as a function of p, and P2 · If P₁ P 2 1 and are the per unit prices of goods 1 and 2, determine the profit maximizing demand of the firm for good 1 as a function of p₁ and p2. Ifp, and p2 are the per unit 1 prices of goods 1 and 2, determine the utility maximizing demand of consumer…Consider a small closed economy with two consumption goods: good 1 (meat) and good 2 (berries). There are two types of agents, h and g, and they have the same preferences over consumption, represented by the utility function: u(x1, 22) = In r1 + In #2. However, there are twice as many type-h agents as type-g agents. The only factors of production are their labour. When a type-h agent chooses to spend a fraction a of his day producing meat and the rest producing berries then his output is (yf, y ) = (2a, 2(1 – a)). A type-g agent is more productive. When she chooses to spend a fraction B of her day producing meat and the rest producing berries then her output is (v7, y2) = (38, 12(1 – B)). Which of the following statements is correct? a. Given equilibrium price p, each agent of type h demands one unit of good 1 (meat) and p units of good 2 (berries). Each agent of type g demands 6/p units of good 1 (meat) and 6 units of good 2 (berries). O b. Given equilibrium price p, each agent of…Consider a two-person, two good pure exchange economy. A's preferences over consumption bundles (x₁, x₂) are represented by the utility function UA (X₁, X₂) = x₁Xz B's preferences over consumption bundles are represented by the utility function UB (X₁, X₂) = x₁ + 2x₂ The initial endowment in goods x, and x₂ are given as: Individual A's as e^ = (1,0.5) and Individual B's as eB= (1, 1.5) 1. Draw an Edgeworth box indicating the endowment and preferences of this problem. 2. Find the set of Pareto Optimal Allocations in this economy and depict these in the Edgeworth box. MRSA = JUA/ƏX₁ X2 aUA/aX₂ X1 ƏUB/0x₁ MRSB = = 2 aUB/0x₂ Therefore, the set of all points where the MRS are equal are given by = 2 → X₂ = 2x1 Show Transcribed Text Advanced Microeconomics. Solve step by step so that I grasp the concept